No, he probably shouldn’t have said it. But it’s true. Republicans, in rushing the tax bill to passage, kept fairly quiet about the fact that they were killing the “individual mandate” and thereby removing the engine that made the Affordable Care Act work. In doing so, they threw the health-care system into chaos without offering any remedy. And Trump just claimed paternity of the destruction.

Trump, in a Cabinet meeting earlier Wednesday, let his fleeting encounter with honesty get the better of him when he read aloud the stage directions that called for Republicans not to advertise that they were killing Obamacare. “Obamacare has been repealed in this bill. We didn’t want to bring it up,” he said. “I told people specifically, ‘Be quiet with the fake-news media because I don’t want them talking too much about it.’ Because I didn’t know how people would … .” Trump didn’t finish that thought, but he said he could admit what had been done “now that it’s approved.”

With those admissions now on tape, Trump has officially claimed full ownership of the health-care system for himself and fellow Republicans. Whatever it is now — or isn’t — is Trumpcare. Here are some of its features:

— Premiums for the most popular health insurance on the individual market exchanges are estimated to rise 34 percent on average next year, according to the consulting firm Avalere Health, because of previous sabotage done by the Trump administration. Premiums in Iowa would be up 69 percent, Wyoming 65 percent and Utah 64 percent.

— Employer-based health insurance costs are forecast to rise in 2018 by the most since 2011, at 4.3 percent, according to the human resources consulting firm Mercer, and overall medical costs will be up 6.5 percent, the first increase in the rate in three years, according to the consulting firm PwC. Assuming those increases are passed along to workers, they would eat up half of the $910 tax cut received next year by households with income between $55,000 and $93,000 and all of the tax cut received by households earning $27,000 to $54,000.

The more Trump claims to have done away with Obamacare, “the more he owns problems in the health system of his making or not,” says Drew Altman, head of the Kaiser Family Foundation and an authority on health care and public opinion. Altman tells me Trump will “certainly own” responsibility for premium increases on the former Obamacare exchanges and for the up to 13 million who will no longer have coverage under the new tax plan.

The new system also belongs to Republicans such as Sen. Susan Collins, R-Maine, who, in exchange for her vote for the tax bill, was hornswoggled into believing Congress will take action before year end on subsidies to stabilize the former Obamacare exchanges. That has now been put off until next year, and it will meet stiff resistance from Collins’s fellow Republicans.

This will be but one source of division among Republicans now that they have secured the tax cut, which was a rare source of unity within the party — and the main reason many GOP lawmakers who find Trump distasteful have stuck with him until now.

Trump and congressional leaders, walking along the White House driveway Wednesday afternoon to “Hail to the Chief,” applauded GOP lawmakers around the South Portico, and the lawmakers applauded back. But soon they will be fighting about immigration, funding the government, cutting Medicare and attacking special counsel Robert Mueller. The divisions will only worsen if Trump continues to have bouts of unaccustomed honesty, as he did Wednesday.

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In addition to his confession about Obamacare, he also acknowledged that “the tax cuts supersede” reform in the tax bill and that “the biggest factor in this plan” is the cut in the corporate tax rate from 35 percent to 21 percent.

Trump did not trespass long in the land of truth. He also renewed his claim that the tax bill is “the largest tax cut in the history of our country.” It isn’t that, by a long shot. But it is many other things, including a huge shock to the health-care system, with no remedy in sight.